One of the basic uses of Cuisenaire Rods is to provide a model for the numbers 1 to 10. If the white rod is assigned the value of 1, the red rod is assigned the value of 2 because the red rod has the same length as a “train” of two white rods. Similarly, the rods from light green through orange are assigned values from 3 through 10, respectively. The orange and white rods can provide a model for place value. To find the length of a certain train, students can cover the train with as many orange rods as they can and then fill in the remaining distance with white rods; so a train covered with 3 orange rods and 4 white rods is 34 white rods long. The rods can be placed end to end to model addition. For example 2 plus 3 can be found by first making a train with a red rod (2) and a light green rod (3) and then finding the single rod (yellow) whose length (5) is equal in length to the 2-rod train. This model corresponds to addition on a number line.
The rods can also be used for acting out subtraction as the search for a missing addend. For example, 5 minus 2 can be found by placing a red rod (2) on top of a yellow (5), then looking for the rod which, when placed next to the red, makes a train equal in length to the yellow.
Multiplication, such as 5 times 2, is interpreted as repeated addition by making a train of 5 red rods or of 2 yellow rods.
Division, such as 10 divided by 2, may be interpreted as repeated subtraction (“How many red rods make a train as long as an orange rod?”) or as sharing (“Two of what color rod make a train as long as an orange rod?”).
Cuisenaire Rods also make effective models for decimals and fractions. If the orange rod is designated as the unit rod, then the white, red, and light green rods represent 0.1, 0.2, and 0.3, respectively. If the dark green rod is chosen as the unit, then the white, red, and light green rods represent 1⁄6, 2⁄6 (1⁄3), and 3⁄6 (1⁄2), respectively. Once the unit rod has been established, addition, subtraction, multiplication, and division of decimals and fractions can be modeled in the same way as the operations with whole numbers.
Cuisenaire Rods are suitable for a variety of geometric and measurement investigations. Once students develop a sense that the white rod is 1 centimeter long, they have little difficulty in accepting and using centimeters as units of length. Since the face of the white rod has an area of 1 square centimeter, the rods are ideal for finding area in square centimeters. Since the volume of the white rod is 1 cubic centimeter, the rods can exemplify the meaning of volume as students use rods to fill up boxes. Students may even develop a sense of a milliliter as the capacity of a container that holds exactly one white rod. Cuisenaire Rods offer many possibilities for forming and discovering number patterns both through creating designs that are growing according to some pattern and through finding the number of ways in which a rod can be made as the sum of other rods. This second scenario can lead to the concept of factors of a number and prime numbers.
The rods also provide a context for building logical reasoning skills. For example, students can use 2 loops of string to create a Venn Diagram showing the multiples of both red and light green rods (which represent 2 and 3, respectively) by placing the multiples of red (red, purple, dark green, brown, and orange) in 1 loop, the multiples of light green (light green, dark green, and blue) in the other loop